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On S*-Quasinormal Subgroups of Prime Power Order in Finite Groups
by Guo Zhong   Bin Xiao   Junpei Luo

Vol. 11 No. 2 (2016) P.359~P.369

ABSTRACT

Let $H$ be a subgroup of a finite group $G.$ We say that $H$ is $S^*$-quasinormal in $G$ if there is a normal subgroup $K$ of $G$ such that $HK\unlhd G$ and $H \cap K \leq H_{seG,}$ where $H_{seG}$ denotes the subgroup of $H$ generated by all those subgroups of $H$ which are $S$-quasinormally embedded in $G.$ In this paper, we investigate the influence of $S^*$-quasinormal subgroups on the $p$-nilpotency of finite groups. Some recent results are extended and generalized.

KEYWORDS
S-quasinormally embedded subgroups, S*-quasinormal subgroups, p-nilpotent groups.

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 20D10, 20D20

MILESTONES